What share of US manufacturing firms export?

What share of US manufacturing firms export? That’s a simple question. But my answer recently changed by quite a lot. While updating one of my class slides that is titled “very few firms export”, I noticed a pretty stark contrast between the old and new statistics I was displaying. In the table below, the 2002 numbers are from Table 2 of Bernard, Jensen, Redding, and Schott (JEP 2007), which reports that 18% of US manufacturing firms were exporters in 2002. The 2007 numbers are from Table 1 of Bernard, Jensen, Redding, and Schott (JEL 2018), which reports that 35% of US manufacturing firms were exporters in 2007.

NAICS Description Share of firms Exporting firm share Export sales share of exporters
2002 2007 2002 2007 2002 2007
311 Food Manufacturing 6.8 6.8 12 23 15 21
312 Beverage and Tobacco Product 0.7 0.9 23 30 7 30
313 Textile Mills 1.0 0.8 25 57 13 39
314 Textile Product Mills 1.9 2.7 12 19 12 12
315 Apparel Manufacturing 3.2 3.6 8 22 14 16
316 Leather and Allied Product 0.4 0.3 24 56 13 19
321 Wood Product Manufacturing 5.5 4.8 8 21 19 09
322 Paper Manufacturing 1.4 1.5 24 48 9 06
323 Printing and Related Support 11.9 11.1 5 15 14 10
324 Petroleum and Coal Products 0.4 0.5 18 34 12 13
325 Chemical Manufacturing 3.1 3.3 36 65 14 23
326 Plastics and Rubber Products 4.4 3.9 28 59 10 11
327 Nonmetallic Mineral Product 4.0 4.3 9 19 12 09
331 Primary Metal Manufacturing 1.5 1.5 30 58 10 31
332 Fabricated Metal Product 19.9 20.6 14 30 12 09
333 Machinery Manufacturing 9.0 8.7 33 61 16 15
334 Computer and Electronic Product 4.5 3.9 38 75 21 28
335 Electrical Equipment, Appliance 1.7 1.7 38 70 13 47
336 Transportation Equipment 3.4 3.4 28 57 13 16
337 Furniture and Related Product 6.4 6.5 7 16 10 14
339 Miscellaneous Manufacturing 9.1 9.3 2 32 15 16
Aggregate manufacturing 100 100 18 35 14 17

 

Did a huge shift occur between 2002 and 2007? No. The difference between these two tables is due to a change in the data source used to identify whether a firm exports. In their 2007 JEP article, BJRS used a question about export sales in the Census of Manufactures (CM). In their 2018 JEL article, BJRS used customs records from the Longitudinal Firm Trade Transactions database (LFTTD) that they built. Footnote 23 of the latter article notes that “the customs records from LFTTD imply that exporting is more prevalent than would be concluded based on the export question in the Census of Manufactures.”

This is a bit of an understatement: only about half of firms that export in customs records say that they export when asked about it in the Census of Manufactures! [This comparison is inexact because the share of exporting firms may have really increased from 2002 to 2007, but BJRS (2018) say that they “find a relatively similar pattern of results for 2007 as for 2002” when they use the CM question for both years.] The typical three-digit NAICS industry has the share of firms that export roughly double when using customs data rather than the Census of Manufactures survey response. Who knows what happened in “Miscellaneous Manufacturing” (NAICS 339), which had 2% in the 2002 CM and 35% in the 2007 LFTTD.

I presume that the customs records are more reliable than the CM question. More firms are exporters than I previously thought!

Trade JMPs (2018-2019)

It’s already November again. Time flies. As I do annually, I’ve gathered a list of trade-related job-market papers. The market leader in trade this year is Penn State, which offers seven candidates. If I’ve missed someone, please contribute to the list in the comments. A few schools (e.g., UCLA, Yale) have not yet posted candidates.

[Nov 11 update: I’ve added a number of candidates since this was posted Nov 5. Now listing 40 people. I didn’t recompute stats nor word cloud.]

Of the 33 candidates I’ve initially listed, 16 use Google Sites, 8 registered their own domain, and only 5 use school-provided webspace (3 use Weebly; 1 GitHub).

Here’s a cloud of the words that appear at least twice in these papers’ titles:

tradejmps20182019wordcloud.png

Why I encourage econ PhD students to learn Julia

Julia is a scientific computing language that an increasing number of economists are adopting (e.g., Tom Sargent, the NY FRB). It is a close substitute for Matlab, and the cost of switching from Matlab to Julia is somewhat modest since Julia syntax is quite similar to Matlab syntax after you change array references from parentheses to square brackets (e.g., “A(2, 2)” in Matlab is “A[2, 2]” in Julia and most other languages), though there are important differences. Julia also competes with Python, R, and C++, among other languages, as a computational tool.

I am now encouraging students to try Julia, which recently released version 1.0. I first installed Julia in the spring of 2016, when it was version 0.4. Julia’s advantages are that it is modern, elegant, open source, and often faster than Matlab. Its downside is that it is a young language, so its syntax is evolving, its user community is smaller, and some features are still in development.

A proper computer scientist would discuss Julia’s computational advantages in terms of concepts like multiple dispatch and typing of variables. For an unsophisticated economist like me, the proof of the pudding is in the eating. My story is quite similar to that of Bradley Setzler, whose structural model that took more than 24 hours to solve in Python took only 15 minutes using Julia. After hearing two of my computationally savvy Booth colleagues praise Julia, I tried it out when doing the numerical simulations in our “A Spatial Knowledge Economy” paper. I took my Matlab code, made a few modest syntax changes, and found that my Julia code solved for equilibrium in only one-sixth of the time that my Matlab code did. My code was likely inefficient in both cases, but that speed improvement persuaded me to use Julia for that project.

For a proper comparison of computational performance, you should look at papers by S. Boragan Aruoba and Jesus Fernandez-Villaverde and by Jon Danielsson and Jia Rong Fan. Aruoba and Fernandez-Villaverde have solved the stochastic neoclassical growth model in a dozen languages. Their 2018 update says “C++ is the fastest alternative, Julia offers a great balance of speed and ease of use, and Python is too slow.” Danielsson and Fan compared Matlab, R, Julia, and Python when implementing financial risk forecasting methods. While you should read their rich comparison, a brief summary of their assessment is that Julia excels in language features and speed but has considerable room for improvement in terms of data handling and libraries.

While I like Julia a lot, it is a young language, which comes at a cost. In March, I had to painfully convert a couple research projects written in Julia 0.5 to version 0.6 after an upgrade of GitHub’s security standards meant that Julia 0.5 users could no longer easily install packages. My computations were fine, of course, but a replication package that required artisanally-installed packages in a no-longer-supported environment wouldn’t have been very helpful to everyone else. I hope that Julia’s 1.0 release means that those who adopt the language now are less likely to face such growing pains, though it might be a couple of months before most packages support 1.0.

At this point, you probably should not use Julia for data cleaning. To be brief, Danielsson and Fan say that Julia is the worst of the four languages they considered for data handling. In our “How Segregated is Urban Consumption?” code, we did our data cleaning in Stata and our computation in Julia. Similarly, Michael Stepner’s health inequality code relies on Julia rather than Stata for a computation-intensive step and Tom Wollmann split his JMP code between Stata and Julia. At this point, I think most users would tell you to use Julia for computation, not data prep. (Caveat: I haven’t tried the JuliaDB package yet.)

If you want to get started in Julia, I found the “Lectures in Quantitative Economics” introduction to Julia by Tom Sargent and John Stachurski very helpful. Also look at Bradley Setzler’s Julia economics tutorials.

Trade economists might be interested in the Julia package FixedEffectModels.jl. It claims to be an order of magnitude faster than Stata when estimating two-way high-dimensional fixed-effects models, which is a bread-and-butter gravity regression. I plan to ask PhD students to explore these issues this fall and will report back after learning more.

The top five journals in economics are accessible, if authors share

I tweeted this, but a blog post seems more appropriate (screenshots of URLs are unhelpful, tweets aren’t indexed by Google, etc).

The top five journals in economics permit authors to either post the published PDF on their personal website or provide a free-access link to the published article.

  • American Economic Review: “Authors are permitted to post published versions of their articles on their personal websites.”
  • Econometrica: “Authors receive a pdf copy of the published article which they can make available for non-commerial use.”
  • Journal of Political Economy: “Authors may also post their article in its published form on their personal or departmental web.”
  • Quarterly Journal of Economics and Review of Economic Studies: “Upon publication, the corresponding author is sent a free-access link to the online version of their paper. This link may be shared with co-authors and interested colleagues, and posted on the author’s personal or institutional webpage.”

Thus, articles in the top five economics journals are accessible to the general public at no fee, provided that the authors of those articles make the effort to share them. Other journals may not be so accessible. A lot of field journals are published by Elsevier, which has less generous sharing policies.

Is it easier to liberalize agriculture via bilateral or multilateral deals?

Tyler Cowen’s latest Bloomberg column is about bilateral trade deals. He’s more optimistic than most:

The smartest case for trade bilateralism is that trade in many goods is already fairly free, but some egregious examples of tariffs and trade barriers remain. Look at agriculture, European restrictions on beef hormones in beef, and the Chinese unwillingness to allow in foreign companies. Targeted strategic bargaining, backed by concrete threats emanating from a relatively powerful nation — in this case the U.S. — could demand removal of those restrictions. Furthermore, the negotiating process would be more directly transactional and less cartelized and bureaucratic.

With regard to liberalizing agriculture, I think the conventional wisdom is that multilateral negotiations are superior. Here’s Jagdish Bhagwati talking to the NY Times back in 2004:

The only way concessions can be made on agricultural subsidies is if you go multilateral. Think of production subsidies, which the United States has: they can’t be cut for just one trading partner. When it comes to export subsidies–which are the big issue for the Europeans and a little bit for us too–we will cut export subsidies say, for Brazil, in a bilateral negotiation, but the Europeans won’t. Then the Europeans will have an advantage. My point is that if subsidies are the name of the game in agriculture, if the foreign countries that export want to remove subsidies, they have to go multilateral.

 

On “hat algebra”

This post is about “hat algebra” in international trade theory. Non-economists won’t find it interesting.

What is “hat algebra”?

Alan Deardorff’s Glossary of International Economics defines “hat algebra” as

The Jones (1965) technique for comparative static analysis in trade models. Totally differentiating a model in logarithms of variables yields a linear system relating small proportional changes (denoted by carats (^), or “hats”) via elasticities and shares. (As published it used *, not ^, due to typographical constraints.)

The Jones and Neary (1980) handbook chapter calls it a circumflex, not a hat, when explaining its use in proving the Stolper-Samuelson theorem:

a given proportional change in commodity prices gives rise to a greater proportional change in factor prices, such that one factor price unambiguously rises and the other falls relative to both commodity prices… the changes in the unit cost and hence in the price of each commodity must be a weighted average of the changes in the two factor prices (where the weights are the distributive shares of the two factors in the sector concerned and a circumflex denotes a proportional change)… Since each commodity price change is bounded by the changes in both factor prices, the Stolper-Samuelson theorem follows immediately.

I’m not sure when “hat algebra” entered the lexicon, but by 1983 Brecher and Feenstra were writing “Eq. (20) may be obtained directly from the familiar ‘hat’ algebra of Jones (1965)”.

What is “exact hat algebra”?

Nowadays, trade economists utter the phrase “exact hat algebra” a lot. What do they mean? Dekle, Eaton, and Kortum (2008) describe a procedure:

Rather than estimating such a model in terms of levels, we specify the model in terms of changes from the current equilibrium. This approach allows us to calibrate the model from existing data on production and trade shares. We thereby finesse having to assemble proxies for bilateral resistance (for example, distance, common language, etc.) or inferring parameters of technology.

Here’s a simple example of the approach. Let’s do a trade-cost counterfactual in an Armington model with labor endowment L, productivity shifter \chi, trade costs \tau, and trade elasticity \epsilon. The endogenous variables are wage w, income Y = w \cdot L, and trade flows X_{ij}. The two relevant equations are the market-clearing condition and the gravity equation.

Suppose trade costs change from \tau_{ij} to \tau'_{ij}, a shock \hat{\tau}_{ij} \equiv \frac{\tau'_{ij}}{\tau_{ij}}. By assumption, \hat{\chi}=\hat{L}=1. We’ll solve for the endogenous variables \hat{\lambda}_{ij}, \hat{X}_{ij} and \hat{w}_{i}. Define “sales shares” by \gamma_{ij}\equiv\frac{X_{ij}}{Y_{i}}. Algebraic manipulations deliver a “hat form” of the market-clearing condition.

Similarly, let’s obtain “”hat form” of the gravity equation.

Combining equations (1.1) and (1.2) under the assumptions that \hat{Y}_{i}=\hat{X}_{i} and \hat{\chi}=\hat{L}=1, we obtain a system of equations characterizing an equilibrium \hat{w}_i as a function of trade-cost shocks \hat{\tau}_{ij}, initial equilibrium shares \lambda_{ij}, and \gamma_{ij}, and the trade elasticity \epsilon:

If we use data to pin down \epsilon, \lambda_{ij}, and \gamma_{ij}, then we can feed in trade-cost shocks \hat{\tau} and solve for \hat{w} to compute the predicted responses of \lambda'_{ij}.

Why is this “exact hat algebra”? When introducing material like that above, Costinot and Rodriguez-Clare (2014) say:

We refer to this approach popularized by Dekle et al. (2008) as “exact hat algebra.”… One can think of this approach as an “exact” version of Jones’s hat algebra for reasons that will be clear in a moment.

What is “calibrated share form”?

Dekle, Eaton, and Kortum (AERPP 2007, p.353-354; IMF Staff Papers 2008, p.522-527) derive the “exact hat algebra” results without reference to any prior work. Presumably, Dekle, Eaton, and Kortum independently derived their approach without realizing a connection to techniques used previously in the computable general equilibrium (CGE) literature. The CGE folks call it “calibrated share form”, as noted by Ralph Ossa and Dave Donaldson.

A 1995 note by Thomas Rutherford outlines the procedure:

In most large-scale applied general equilibrium models, we have many function parameters to specify with relative ly few observations. The conventional approach is to calibrate functional parameters to a single benchmark equilibrium… Calibration formulae for CES functions are messy and difficult to remember. Consequently, the specification of function coefficients is complicated and error-prone. For applied work using calibrated functions, it is much easier to use the “calibrated share form” of the CES function. In the calibrated form, the cost and demand functions explicitly incorporate

  • benchmark factor demands
  • benchmark factor prices
  • the elasticity of substitution
  • benchmark cost
  • benchmark output
  • benchmark value shares

Rutherford shows that the CES production function y(K,L) = \gamma \left(\alpha K^{\rho} + (1-\alpha)L^{\rho}\right)^{1/\rho} can be calibrated relative to a benchmark with output \bar{y}, capital \bar{K}, and labor \bar{L} as y = \bar{y} \left[\theta \left(\frac{K}{\bar{K}}\right)^{\rho} + (1-\theta)\left(\frac{L}{\bar{L}}\right)^{\rho}\right]^{1/\rho}, where \theta is the capital share of factor income. If we introduce “hat notation” with \hat{y} = y/\bar{y}, we get \hat{y} = \left[\theta \hat{K}^{\rho} + (1-\theta)\hat{L}^{\rho}\right]^{1/\rho}. Similar manipulations of the rest of the equations in the model delivers a means of computing counterfactuals in the CGE setting.

What economic activities are “tradable”?

I’ve had a couple conversations with graduate students in recent months about classifying industries or occupations by their tradability, so here’s a blog post reviewing some of the relevant literature.

A number of papers emphasize predictions that differ for tradable and non-tradable activities. Perhaps the most famous is Atif Mian and Amir Sufi’s Econometrica article showing that counties with a larger decline in housing net worth experienced a larger decline in non-tradable employment.

Mian and Sufi define industries’ tradability by two different means, one yielding a discrete measure and the other continuous variation:

The first method defines retail- and restaurant-related industries as non-tradable, and industries that show up in global trade data as tradable. Our second method is based on the idea that industries that rely on national demand will tend to be geographically concentrated, while industries relying on local demand will be more uniformly distributed. An industry’s geographical concentration index across the country therefore serves as an index of “tradability.”

Inferring tradability is hard. Since surveys of domestic transactions like the Commodity Flow Survey don’t gather data on the services sector, measures like “average shipment distance by industry” (Table 5a of the 2012 CFS) are only available for manufacturing, mining, and agricultural industries. Antoine Gervais and Brad Jensen have also pursued the idea of using industries’ geography concentration to reveal their tradability, allowing them to compare the level of trade costs in manufacturing and services. One shortcoming of this strategy is that the geographic concentration of economic activity likely reflects both sectoral variation in tradability and sectoral variation in the strength of agglomeration forces. That may be one reason that Mian and Sufi discretize the concentration measure, categorizing “the top and bottom quartile of industries by geographical concentration as tradable and non-tradable, respectively.”

We might also want to speak to the tradability of various occupations. Ariel Burstein, Gordon Hanson, Lin Tian, and Jonathan Vogel’s recent paper on the labor-market consequences of immigration varying with occupations’ tradability is a nice example. They use “the Blinder and Krueger (2013) measure of `offshorability’, which is based on professional coders’ assessments of the ease with which each occupation could be offshored” (p.20). When they look at industries (Appendix G), they use an approach similar to that of Mian and Sufi.

Are there other measure of tradability in the literature?

Trade JMPs (2017-2018)

It’s that time of year again. As I’ve done since 2010, I’ve gathered a list of trade-related job-market papers. New this year is a small collection of spatial economics papers that aren’t about trade per se. If I’ve missed someone, please contribute to the list in the comments.

Spatial Economics

 

I’m hiring research assistants

If you are a student interested in earning an economics PhD, you should consider working as a research assistant before starting graduate school. Working on someone else’s research projects is an opportunity to learn a lot about the research process that is never taught in PhD courses. Learning by doing is a powerful force.

I’m hiring people to start working with me in summer of 2018.  Apply here: http://www.nber.org/jobs/Dingel_Chicago%20Booth.pdf. More generally, you can find a list of such opportunities on the NBER website.

Co-authoring is not about comparative advantage

Comparative advantage is one of our field’s defining insights and “an essential part of every economist’s intellectual toolkit“. The principle is both true and non-obvious, so understanding it separates those who have taken an economics class from those who have not. While economists are rightfully proud of comparative advantage, there is at least one circumstance in which I think economists overuse it.

If you chat with economists about their co-authored research, you’ll often hear them casually attribute the division of labor within their research team to comparative advantage. I’m sure I’ve said this a number of times myself. But co-authoring is not about comparative advantage.

Suppose producing a paper involves two tasks: solving a model and estimating it. If you are better at both tasks than your co-author, then you ought to do both yourself and break up with your co-author. My advice seems contrary to David Ricardo’s famous insight that there are still gains from specialization and trade when one party has absolute advantage in both tasks. But the optimal assignment of tasks does not always depend on comparative advantage.

The Ricardian production function

The principle of comparative advantage is tied to a particular production function. In the Ricardian model, production functions are linear. Thus, individuals’ marginal products are constant. This fact allows us to describe individuals’ choices in terms of relative productivities and relative prices.

In a Ricardian world, the ordering of task assignments depends only on relative productivities: at any relative price, an individual has comparative advantage in the task in which her relative productivity is higher. Absolute productivities show up in a market-clearing condition that determines the relative prices necessary for supply of each task to equal its demand.

Does this sound like co-authorship? Some of the institutional details are wrong. Co-authors don’t usually pay each other for their output. Adding more people may pay off because each of n co-authors can receive more than 1/n credit. But beyond the unusual features of “selling” your output to academia, the Ricardian model’s description of the production process as a research team just doesn’t fit.

Producing research as a team

As Michael Sattinger (1993) explains, not all assignment models are models of comparative advantage:

Some economists may believe that comparative advantage is the only production principle underlying the assignment of workers to jobs, but this is incorrect. As a counterexample, consider an economy in which a job is associated with the use of a particular machine that can be used by only one person at a time…
The reason comparative advantage does not indicate the optimal assignment in this case is that earnings from a job are no longer proportional to physical output at the job. With cooperating factors of production (either explicit in the form of a machine or implicit via a scarcity in the jobs available), an opportunity cost for the cooperating factor must be subtracted from the value of output to yield the earnings.

In the Ricardian model, absolute disadvantage is not a problem, because quantity can make up for quality. If the laborers assigned to a task have low productivity, more labor can be employed in that task to produce more output. But in many situations, quantity cannot substitute for quality. This is most obvious in sports, where rules constrain team size: a hockey team can only have one goaltender. When jobs are scarce, comparative advantage does not determine the optimal assignment.

In a famous applied theory paper, Michael Kremer explored the consequences of producing in a team in which the number of tasks is fixed, each task may be performed by only one person, and a mistake in any one task diminishes the entire project’s value. The latter feature makes this the “O-Ring Theory of Development”, as the space shuttle Challenger blew up due to the failure of only one of its thousands of components.

This production function sounds more like the economics research process. A paper is a discrete unit of output, and it is likely only as persuasive as its weakest link. Poor writing can totally obfuscate good theory. Rarely can a beautiful theory salvage garbage empirics. And it is hard to believe that input quantity can substitute for input quality: “this paper was written by mediocre theorists, but there were so many of them working on it!”

In Kremer’s O-Ring model, the efficient assignment is that workers of similar skill work together in teams. A great theorist pairs with a great empiricist. As a first pass, this seems a reasonable description of the co-authorships we actually observe.

Co-authoring is not about comparative advantage

Of course, production is more complicated than that. How do we explain the valuable contributions of research assistants to projects when their supervisors (would like to claim that they) have absolute advantage across all tasks? One needs a model of hierarchical or sequential production in which research assistants handle easier problems and then pass on unsolved problems to their supervisors. Luis Garicano, Esteban Rossi-Hansberg, and co-authors have studied these knowledge-based hieararchies in environments ranging from law firms to exporters.

In short, the optimal assignment depends on the nature of the production function. Despite economists’ frequent invocation of our beloved insight, co-authoring is not about comparative advantage.